Robust Bayesian Inference of Causal Effects via Randomization Distributions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| author | Huch, Easton Feinberg, Fred Dempsey, Walter |
| author_facet | Huch, Easton Feinberg, Fred Dempsey, Walter |
| contents | We present a general framework for Bayesian inference of causal effects that delivers provably robust inferences founded on design-based randomization of treatments. The framework involves fixing the observed potential outcomes and forming a likelihood based on the randomization distribution of a statistic. The method requires specification of a treatment effect model; in many cases, however, it does not require specification of marginal outcome distributions, resulting in weaker assumptions compared to Bayesian superpopulation-based methods. We show that the framework is compatible with posterior model checking in the form of posterior-averaged randomization tests. We prove several theoretical properties for the method, including a Bernstein-von Mises theorem and large-sample properties of posterior expectations. In particular, we show that the posterior mean is asymptotically equivalent to Hodges-Lehmann estimators, which provides a bridge to many classical estimators in causal inference, including inverse-probability-weighted estimators and Hájek estimators. We evaluate the theory and utility of the framework in simulation and a case study involving a nutrition experiment. In the latter, our framework uncovers strong evidence of effect heterogeneity despite a lack of evidence for moderation effects. The basic framework allows numerous extensions, including the use of covariates, sensitivity analysis, estimation of assignment mechanisms, and generalization to nonbinary treatments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_00676 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Bayesian Inference of Causal Effects via Randomization Distributions Huch, Easton Feinberg, Fred Dempsey, Walter Methodology We present a general framework for Bayesian inference of causal effects that delivers provably robust inferences founded on design-based randomization of treatments. The framework involves fixing the observed potential outcomes and forming a likelihood based on the randomization distribution of a statistic. The method requires specification of a treatment effect model; in many cases, however, it does not require specification of marginal outcome distributions, resulting in weaker assumptions compared to Bayesian superpopulation-based methods. We show that the framework is compatible with posterior model checking in the form of posterior-averaged randomization tests. We prove several theoretical properties for the method, including a Bernstein-von Mises theorem and large-sample properties of posterior expectations. In particular, we show that the posterior mean is asymptotically equivalent to Hodges-Lehmann estimators, which provides a bridge to many classical estimators in causal inference, including inverse-probability-weighted estimators and Hájek estimators. We evaluate the theory and utility of the framework in simulation and a case study involving a nutrition experiment. In the latter, our framework uncovers strong evidence of effect heterogeneity despite a lack of evidence for moderation effects. The basic framework allows numerous extensions, including the use of covariates, sensitivity analysis, estimation of assignment mechanisms, and generalization to nonbinary treatments. |
| title | Robust Bayesian Inference of Causal Effects via Randomization Distributions |
| topic | Methodology |
| url | https://arxiv.org/abs/2511.00676 |